Step by Step Long Division Calculator

Example 1) Work out 84 ÷ 3

So we are working out \[ 3 \enclose {longdiv} {84} \]

Stage 1

Step 1) Divide

First step is to work out 8 ÷ 3, which means we need to find how many groups of 3 make 8.

We can get 2 groups of 3 in 8 so we write a 2 on the answer line above the 8: \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \end{array} \]

Step 2) Multiply

We multiply the number of groups by the divisor: 2 x 3 = 6 and write this underneath the 8: \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \end{array} \]

Step 3) Subtract

Next we subtract 6 from 8 to get 2 which we write underneath the 6. \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 2 \end{array} \]

Step 4) Bring down

The next step is to bring down the 4 and put it next to the 2 \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \end{array} \]

Stage 2

Step 1) Divide

We now have to work out 24 ÷ 3, or how many groups of 3 make 24.

There are 8 groups of 3 in 24. So we write an 8 on the answer line above the 4: \[ \begin {array}{l} \quad 28 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \\ \end{array} \]

Step 2) Multiply

8 groups of 3 make 24. We write this underneath the 24: \[ \begin {array}{l} \quad 28 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \\ \quad \underline{24} \end{array} \]

Step 3) Subtract

Finally subtract 24 from 24 to give us an answer of 0 which we write underneath the 24. \[ \begin {array}{l} \quad 28 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \\ \quad \underline{24} \\ \quad \; \; 0 \end{array} \]

Step 4) Bring down next digit

There are no more digits to bring down so we have finished. There is a 0 at the bottom of the long division which means there is no remainder.

Answer: 84 ÷ 3 = 28

The fact that there is no remainder means that the dividend, which is 84, is a multiple of the divisor, which is 3, and also that the divisor is a factor of the dividend!

For more information about Factors and Multiples, use the link below:

• Factors and Multiples Support

Example 2) Work out 347 ÷ 4

So we are working out \[ 4 \enclose {longdiv} {347} \]

Stage 1

Step 1) Divide

FIrst step is to work out 3 ÷ 4, which means we need to find how many groups of 4 make 3.

There are 0 groups of 4 in 3, so we write a 0 on the answer line above the 3 then keep the 3 in its place and go on to the next digit which is 4.

This gives us: \[ \begin {array}{l} \quad 0 \\ 4 \enclose {longdiv} {347} \end{array} \]

So we need to work out 34 ÷ 4, or find how many groups of 4 make 34.

We can get 8 groups of 4 in 34 so we write an 8 on the answer line above the 4.

This gives us: \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \end{array} \]

Step 2) Multiply

8 groups of 4 make 32. We write this underneath the 34: \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \end{array} \]

Step 3) Subtract

We subtract 32 from 34 to give us an answer of 2 which we put underneath the 32: \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 2 \end{array} \]

Step 4) Bring down next digit

Next we bring the 7 down alongside the 2. \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \end{array} \]

Stage 2

Step 1) Divide

So we need to work out 27 ÷ 4, or find how many 4s make 27.

There are 6 groups of 4 in 27. So we write a 6 on the answer line above the 7: \[ \begin {array}{l} \quad 086 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \end{array} \]

Step 2) Multiply

6 groups of 4 make 24. We write this underneath the 27: \[ \begin {array}{l} \quad 086 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \\ \quad \; \; \underline {24} \end{array} \]

Step 3) Subtract

Finally we need to subtract 24 from 27 to give us 3 which we put underneath the 24.

\[ \begin {array}{l} \quad 086 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \\ \quad \; \; \underline {24} \\ \quad \quad 3 \end{array} \]

Step 4) Bring down next digit

There are no more digits to bring down so we have finished. The 3 at the bottom of the long division is the remainder.

Answer: 347 ÷ 4 = 86r3

If we wanted the remainder as a fraction, we would have 347 ÷ 4 = 86 ¾

Example 3) Work out 8165 ÷ 12

So we are working out \[ 12 \enclose {longdiv} {8165} \]

Stage 1

Step 1) Divide

FIrst step is to work out 8 ÷ 12, which means we need to find how many groups of 12 make 8.

There are 0 groups of 12 in 8, so we keep the 8 in its place and put a zero above the 8 then go on to the next digit which is 1.

This gives us: \[ \begin {array}{l} \quad \; 0 \\ 12 \enclose {longdiv} {8165} \end{array} \]

So the next step is to work out 81 ÷ 12, or find how many groups of 12 make 81.

There are 6 groups of 12 in 81, so we put a 6 above the 1.

This gives us: \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \end{array} \]

Step 2) Multiply

6 groups of 12 make 72. We write this underneath the 81. \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \end{array} \]

Step 3) Subtract

We subtract 72 from 81 to get 9 which goes underneath the 72: \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 9 \end{array} \]

Step 4) Bring down next digit

Next we bring the 6 down alongside the 9. \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \end{array} \]

Stage 2

Step 1) Divide

So we need to work out 96 ÷ 12, or find how many 12s make 96.

There are 8 groups of 12 in 96, so we write 8 in the answer line above the 6. \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \end{array} \]

Step 2) Multiply

8 groups of 12 make 96 which we write underneath: \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \end{array} \]

Step 3) Subtract

Now we subtract 96 from 96 to give us 0. \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 0 \end{array} \]

Step 4) Bring down next digit

Now we bring down the 5. \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \end{array} \]

Stage 3

Step 1) Divide

Nexy we need to work out 5 ÷ 12, or how many 12s make 5.

There are 0 groups of 12 in 5, so we write 0 above the 5 digit in the answer line: \[ \begin {array}{l} \quad \; 0680 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \\ \end{array} \]

Step 2) Multiply

0 groups of 12 make 0, so we write 0 under the 05: \[ \begin {array}{l} \quad \; 0680 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \\ \qquad \; \: \underline {00} \end{array} \]

Step 3) Subtract

Subtracting 0 from 5 gives us 5. \[ \begin {array}{l} \quad \; 0680 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \\ \qquad \; \: \underline {00} \\ \qquad \quad 5 \end{array} \]

Step 4) Bring down next digit

There are no more digits to bring down so we have finished. The 5 at the bottom of the long division is the remainder.

Answer: 8165 ÷ 12 = 680r5

If we wanted the remainder as a fraction, we would have \[ 8165 \div 12 = 680 {5 \over 12} \]